| DATE |
Description |
|---|---|
Wed Jan 17 |
Intro to IDL. Datatypes, structures. Sav files, FITS files. The GSFC website and other accessible libraries. The startup file. Paths. Managing IDL on multiple platforms. Color schemes--RBG and CMYK. Visual classes: Pseudocolor, Truecolor, Directcolor. Color tables. Using color in plots. |
Mon Jan 22 |
Basic image display and processing on Xwindow. Making PostScript files of plots and images. |
Wed Jan 24 |
Color images: one-dimensional, two-d, and three-d. Annotating images. Introduction to Projections |
Mon Jan 29 |
Recap of eclipse problem. Projections. Monovariate PDFs and their transformations. |
Wed Jan 31 |
Customized random number generators. Monte Carlo basics. Bivariate PDF's and their transformations. |
Mon Feb 5 |
Review homework. Bivariate PDF transformations -- three examples. Three important monovariate PDFs: Binomial, Poisson, Gaussian. |
Wed Feb 7 |
Discrete distributions. The chi-square PDF. Reduced chi-square. Using chi-square to define the probability that the input data follows the model. |
Mon Feb 12 |
Statistical tests for PDFs: the KS and chi-square tests. Introduction to multivariate Gaussian statistics and covariance. |
Wed Feb 14 |
Multivariate Gaussian statistics. Discrete distributions: mean, variance, variance of variance. Introduction to covariance. |
Mon Feb 19 |
Emporer's day (the former President's day) holiday; NO CLASS. |
Wed Feb 21 |
Error propagation including covariance. Transformation of variables, Eigenvector diagonalizing the covariance matrix. Short topic: bits, bytes, idl variable types and organizational structure types. |
Mon Feb 26 |
Finish the 'short topic' from Feb 21. Maximum Likelihood (ML) for Gaussian and double-sided exponential statistics. Virtues of the median. Three waays to express uncertainty (sigma, confidence, and Delta chisq). |
Wed Feb 28 |
More on Delta chisq as an uncertainty measure. Examples of linear and nonlinear ML. Example of interpreting and expressing results of poisson statistics. |
Mon Mar 5 |
Nonlinear ML for a single parameter. Introduction to multivariatee Least-squares fitting; |
Wed Mar 7 |
illustrative example of least-squares: a polynomial fit. covariance. orthogonal functions; legendree fit. formulating least squares properly: two examples. Looking at the matrices to chase down problems. Proof (and conditions required) for the covariance matrix to reflect the true covariance. |
Mon Mar 12 |
HAWKING LECTURE: NO CLASS |
wED Mar 14 |
Nonlinear least-squares fitting using Taylor expansion. Multiple minima. Numerical derivatives: accuracy considerations. |
Mon Mar 19 |
Fitting arbitrary curves with rational functions. Cubic splines. Least squares with cubic splines: bsplines. |
Wed Mar 21 |
Finish bsplines. Least squares cubic splines using Schlegel/Burles IDL procedure "bspline_iterfit". Use of Singular Value Decomposition to handle degeneracies in least-squares fitting. |
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Mon Apr 2 |
Chi-square fitting and weighted fitting. Covariance and error degree of confidence for multivariate fitting. |
Wed Apr 4 |
Finish chi-square covariance discussion. Weighted iterative fitting: constraints; a modified Chauvenet's criterion. |
Mon Apr 9 |
Minimum Absolute Residual Sum (MARS) fitting. Fitting when there is no independent variable--all variables have uncertainties. |
Mon Apr 16 |
Fourier transforms: basic math aspects. A few important transform pairs. Scaling and shift theorem. convolution and correlation theorems with real-life astronomical examples. |
Wed Apr 18 |
Digital Fourier transforms. Sampling, aliasing, leakage, binning. Example of crab optical pulsar data. Wiener filtering, optimum filtering. The FFT. Interpolating power spectra. |
Mon Apr 23 |
NO CLASS -- CARL'S AT A MEETING! |
Wed Apr 25 |
Finish covering the material in the previous class. Irregular sampling with Fourier. the Lomb periodogram. The window function. examples, clean. |
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Mon Apr 24 |
Digital correlators in radio astronomy; gratings in optical astronomy. Digital convolution and correlation Deconvolution, noise, Wiener filtering |
Mon May 1 |
More irregular sampling: maximum entropy. |
Wed May 3 |
Wavelets I: continuous wavelets |
Mon May 8 |
Wavelets II: discrete wavelets. |
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